Recent work on causal learning has investigated the possible role of generic priors in guiding human judgments of causal strength. One proposal has been that people have a preference for causes that are sparse and strong—i.e., few in number and individually strong (Lu et al., 2008). Evidence for the use of sparse-and-strong priors has been obtained using a maximally simple causal set-up (a single candidate cause plus unobserved background causes). Here we examine the possible impact of generic priors in more complex, multi- causal set-ups. Sparse-and-strong priors predict that competition can be observed between candidate causes even if they occur independently (i.e., the estimated strength of cause A will be lower if the strength of uncorrelated cause B is high rather than low). Experiment 1 revealed such a cue competition effect in judgments of causal strength. Experiment 2 showed that, as predicted by a Bayesian learning model with sparse-and-strong priors, the impact of the prior diminishes as sample size increases. These findings support the importance of a preference for parsimony as a constraint on causal learning.